Magnetic fields

Magnetic fields

• Magnetic field of a planet (Earth)• Dipole• Higher orders• Short period variations• Secular variations• Polar drift• Paleomagnetism• Magnetic fields of other planets• Remnant fields

Reference:Physics of the Earth, F. D. Stacey & P. M. Davis, Cambridge

University Press, 2008

Magnetic fields of a planet

• Many planets/moons have a magnetic field

• In first order it is a dipolar field, higher orders exist

• The source is inside the planet• The magnetic field axes do not

necessarily coincide with the rotation axis of the planet

• The dipole centre can be offset from the planetary centre

• The magnetic field is variable on any timescale [ms – Myears]

• The pole direction can reverse• A planetary magnetic field can

vanish if the driving mechanism is diminished (e.g. Mars)

Field intensity of the Earth magnetic field

Image: NOAA/NGDC & CIRES

Field declination

Field inclination

Historical

• Magnetic properties of lodestones were recognised already by ~600BC

• It was attributed to a effluvium in Greece or qi in China which was essentially a life energy

• Initially only the horizontal orientation (declination) was used for navigation

• The magnetic declination i.e. the deviation of the magnetic poles from the geographic poles was recognised and applied in navigation maps in the 16th century

• The inclination of the magnetic field was confirmed in the 16th century but still was disputed later on

• At 1600 the magnetic field of spherical lodestones was described as a quadrupole field (W. Gilbert, De Magnete, 1600, ISBN-10: 048626761X )

• Secular variations were reported from the 15 - 16th century on• The magnetic field as an internal field was confirmed not before the

early 20th century and was contested by e.g. Einstein until 1940

Left: HM 46. PORTOLAN ATLAS and NAUTICAL ALMANAC. France, 1543Right: De Magnete 1628 Edition

Field creation mechanism

• A planetary magnetic field is assumed to be created by electric currents in a liquid electrical conducting part of the outer core.

• The magnetic induction equation describes the field creation by a moving fluid

• ηm is the magnetic diffusivity,• σ electrical conductivity,• μ magnetic permeabiltiy,• v fluid velocity which is sustained by convection• When v → 0 the dipole would vanish within some tens of thousands

years

1

2

BvBtB

m

Image: USGS

Field propagation & attenuation

• Field generated in core < Re/2• Small scale features are hidden

because of distance to surface and magnetisation in crust

• Electrical conductivity in mantle is contributing to field attenuation– (Gaillard et al. Carbonatite Melts

and Electrical Conductivity in the Asthenosphere. Science, 2008; 322 (5906): 1363 DOI: 10.1126/science.1164446)

• Unmaintained electric currents in the core would decay due to ohmic dissipation within 104 years

Electrical conductivity map of earth mantle. Image:  Anna Kelbert, Oregon State University 2009

Best fitting dipole

• A planetary magnetic field can (mostly) be represented in first order by a dipole field with the magnetic moment m

• The magnetic potential Vm of the best fitting dipole is

222 Am10768.7

Earthm

iAm

Äquator5

30

0

30

0

300

0

23

ra Gauss3004.0T10004.34

cos24

sin4

4cos

4

amB

rm

rVBr

rmV

rB

gradVBr

mrrmV

Earth

m

m

m

m

Non dipole elements

• About 20% of earths magnetic field are contributions from higher pole orders.

• Spherical harmonic coefficients for a internal field can be found using:

• The coefficients g and h are given in nanoTesla (nT) and can be derived from satellite measurements

• The angle η between the magnetic and geographic axes is 10.26°

cossincos1 0

1

0Phg m

ll

l

m

m

l

m

l

l

m lmmraaV

26.10192.0tan

01

211

211

211

211

2010

ghg

hggB

Short period variations

• Short period variations are mostly induced by external events– Solar Flares– Magnetic storms in the

solar wind

• -> See next unit on magnetospheres and solar planetary interactions

Secular variations

• Changing patterns in the core motion drive slow variations in the magnetic field (> 1 year)

• Most extra-terrestrial effects are short periodic

• Changes are not uniform on a global scale

• Currently we observe a field drift of about 0.2°/year for the higher harmonics

• The total field strength over the last centuries has decreased by ~6.3%/century

• Over geological timescales pole reversals have been found

Paleomagnetism

• Iron rich lava can trap the current local magnetic field direction while cooling

• The paleomagnetic field can be reconstructed from bore stems

Polar drift

• Over geologic timescales the position of the magnetic poles can change

• Thus far about 170 polar reversals have been found

• Today the north pole is moving towards Siberia with an average speed of 10 km/year

• Recently the speed has increased to ~40 km/year

Magnetic fields of other planets

Magnetic fields of other planets

Planet Dipole Moment [Am2] Dynamo Surface Field [nT]

Mercury 5x1019 probable 457

Venus <4x1018 No <2.5

Earth 8x1022 Yes 41455

Mars ~1x1018 No 3.5

Jupiter 1.6x1027 Yes 650000

Saturn 4.7x1025 Yes 32850

Uranus 3.8x1024 Yes 32170

Neptune 2.0x1024 Yes 18560

Remnant Magnetic Field of Mars

• Due to the lack of plate tectonics i.e. large internal convection the dynamo process on Mars has stopped

• The remnant magnetic field is very weak and consists mostly of multi-pole contributions

• The paleomagnetic field was observed from orbit by the MGS orbiter in 1999

Image: MGS/NASA

Magnetic field of the Moon

Induced magnetic field

• The solar wind can produce an induced magnetic field around planets/moons with an atmosphere or rather an ionosphere

• E.g. Venus and Titan when outside the Saturn magnetosphere

Image: MPS, M. Fränz